That $500 million profit sounds like a big chunk of change. But fewer than 25 athletics departments at the nation’s 228 NCAA Division I public schools are in the black. The profit is almost completely produced by two sports – football and basketball – and even those programs lose money at many schools.

The money made on the gridiron and court is used to support athletes who play soccer, golf, field hockey and other non-revenue sports.

The current system could, of course, be changed to free up funds to pay football and basketball players. Other athletes could take the hit through painful cuts to non-revenue sports. And expenditures for lavish training facilities and coaching salaries could be reduced. That last option seems like low-hanging fruit as many schools now spend more on salaries than on scholarships. USA Today reports that the average salary for head football coaches at major college universities is $1.42 million while their assistants earn an average salary of $200,000. Mike Krzyzewski earns more than $7 million a year coaching Duke basketball.

Perhaps Coach K and his colleagues would be willing to forsake some compensation to reward their athletes. But they might not. Then we might ask: Would their players be willing to trade the chance to work with the best coaches and facilities in exchange for paychecks? That is, after all, one of the main reasons they choose to attend those schools.

This goes to the second false assumption: That the current system exploits athletes. Yes, some of them are being used, but for good purposes: To support their fellow athletes and, indirectly, the academic mission of their schools through the vast sums they inspire alumni to donate.

But these football and basketball players are getting plenty in return. Except for a handful of basketball players, even the most talented athletes are not ready to play professional sports when they graduate high school. Elite players struggle and strive to attend college because it offers them the best chance of upping their game and moving to the next level.

Top players celebrate their admission to Duke, UNC or N.C. State because they receive a range of benefits. These include the chance to hone and display their skills on the biggest stages.

Yes, people tune in to watch great players – but the players are not attracting those eyeballs on their own. They are piggybacking on the rich tradition of excellence those schools have worked hard to attain, as well as the vision of school and league administrators who negotiated the television contracts that put them in the spotlight. Michael Jordan got at least as much out of UNC as the school got out of him.

Of course, the vast majority of athletes at even elite Division I programs do not make it to the pros. But, almost all have the chance to earn degrees at flagship universities. Once there, if needed, they are provided with tutors and other forms of support to help them produce college-level work.

As we all know, no-show classes and over helpful tutors are only some of the abuses in this system. But, from the standpoint of the “exploited” athletes, would they be better off not attending college at all? Would they be better prepared for life if they could go straight to professional minor leagues?

Don’t get me wrong. Some of the modest proposals being discussed sound sensible, including more generous stipends for some athletes, long-term health insurance for chronic sports injuries and more robust efforts to ensure athletes earn their degrees.

But in order to reform the system, we have to understand it. A good place to start is to stop focusing on the illusions of profitable sports and exploited athletes.